Assessing intra- and inter-molecular charge transfer excitations in non-fullerene acceptors using electroabsorption spectroscopy

Organic photovoltaic cells using Y6 non-fullerene acceptors have recently achieved high efficiency, and it was suggested to be attributed to the charge-transfer (CT) nature of the excitations in Y6 aggregates. Here, by combining electroabsorption spectroscopy measurements and electronic-structure calculations, we find that the charge-transfer character already exists in isolated Y6 molecules but is strongly increased when there is molecular aggregation. Surprisingly, it is found that the large enhanced charge transfer in clustered Y6 molecules is not due to an increase in excited-state dipole moment, Δμ, as observed in other organic systems, but due to a reduced polarizability change, Δp. It is proposed that such a strong charge-transfer character is promoted by the stabilization of the charge-transfer energy upon aggregation, as deduced from density functional theory and four-state model calculations. This work provides insight into the correlation between molecular electronic properties and charge-transfer characteristics in organic electronic materials.

ΔE indicates the relative shift (shifting parameter) in excitation energy upon application of the electric field.Δµ= ( 1 − 0 ), the difference in permanent dipole moment (unit -Debye) between ground and excited states.Δp = ( 1 − 0 ), the difference in polarizability (unit -cm 3 ) between ground and excited states.Consequently, measuring the change in absorption under an electrical field (electroabsorption, EA) brings insight into the excitonic properties (Δµ and Δp) of a material.A detailed mathematical derivation of the first and second-harmonic EA equations is given in Supplementary Note 1.

 DFT results for ITIC.
A B Supplementary Fig. 3: Illustration of two distinct dimer configurations of ITIC, labeled as A and B, extracted from the crystal structure reported in the literature 2 .Both dimers have symmetric constituent monomers.We replaced the long side chains with -CH3 groups for our calculations.

 GIWAS & GISAXS results of different loading ratios of Y6 in PVK
To identify the stacking change of PVK and Y6, we use *, #, and + symbols to represent the signals from PVK, Y6, and unclarified, respectively.First, the peaks of PVK (*) shift to the lower q region with an increase in Y6 loading, indicating the stacking between PVK chains is getting looser.It indicates the stronger aggregation of Y6 in the thin film.Second, the π-π peak of Y6 (*) shifts to a higher 'q' region from 70% Y6 loading to pure film, indicating the stacking between the Y6 is getting tighter.Moreover, the peaks labeled by '+' show systematic shifting to the lower q region with the increase in Y6 loading; however, due to the low resolution and overlapping of different peaks, it is challenging to judge whether this peak belongs to PVK or Y6.According to Kasha's model, the interaction between adjacent molecules leads to the energetic splitting of the excited states of the monomer 3 .As shown in the figure, we first fitted the optical absorption of the Y6 solution, where the spectrum predominantly contained non-interacting molecules (dispersed phases 1 and 2).The fitting equation of the absorption spectra with the Frank-Condon-weight density of states (FCWD) in the framework of Marcus-Levich-Jortner theory 4 is expressed as: where  is the Marcus reorganization energy (meV), S is the Huang-Rhys factor accounting for the coupling of the two states, is Boltzmann constant, and E is the energy difference between the oscillation energy and 0-0 transition energy E00 (eV).Two FC progressions with transition energies determined by the peak local maxima at around 1.69 eV (E01) and 2.1 eV (E02) can be well reproduced.A vibrational energy, hω1 = 160 meV, was used on the Raman measurements of Y6 5 .The peak intensity values (A), Huang-Rhys parameter (S), and Gaussian linewidth parameter (λ) were adjusted within a reasonable range of values for different transitions to obtain a good fit.
For thin films having 10 wt% and 100 wt% Y6, we kept the FC parameters of the Y6 solution constant (peaks 1 and 2); four more FC progressions at transition energies ( 03 -06 ) can be found.Since each progression represents the electronic configuration of isolated molecules and different dimers, the FC parameter should be similar in different samples.During the fitting, the values of the transition energies (E), the vibrational energy (hω), the Huang-Rhys parameter ( 1 ), and the Gaussian linewidth parameter (λ) for each progression were kept almost the same for all samples.Only the peak intensity values (A3 to A6) were adjusted to get the best spectral fit.
These fitting results and FC parameters we obtained are very consistent with the results obtained by Köhler and co-workers 6 .The table below shows the FC parameters used for different loading ratios of Y6.
where ΔE < 0 corresponds to a red shift and ΔE > 0 corresponds to a blue shift of the absorption spectrum, and the change in absorption coefficient Δα can be expressed as: where and are the absorption coefficients with and without electric field.
According to the Stark effect, the energy level will shift under electric field F depending on its dipole moment and polarizability (material properties) in its equilibrium state.
The change of absorption coefficient  of a thin film can be expressed as a Taylor series: ∂E 3 are the first, second, and third derivatives of the absorption coefficient, respectively.To derive the electroabsorption equation in terms of Δµ and Δp, we can substitute eqn.(5) into eqn.( 6), In eqn.( 7), as we focus on the first and second derivative terms, the higher-order derivatives are neglected, i.e.: In order to formulate the first and second harmonic EA equations, eqn.( 8) is substituted by the applied electric field with the superposition of an AC and DC components as In eqn.( 9), the DC, sin ωt, and2 ωt terms contribute to the zero, first, and second harmonic signals, respectively, i.e.:  Zeroth harmonic terms  First harmonic terms By rearranging the terms related to the first and second harmonic EA equations, The last term where d is the thickness of the active layer.
Substituting eqn.( 16) into eqn.( 14) and ( 15), i.e.: Equations ( 17) and ( 18) can be further expressed in terms of device absorbance by replacing the absorption coefficient α as described below: Converting absorption coefficient into device absorbance ( ), Rewriting the first and second harmonic EA equations in terms of transmittance (T) and :  First harmonic EA fitting equation In addition, in case there is no preferred dipole orientation, the first and second harmonic should have the same spectral characteristics and their ratio is simply proportional to the applied DC and AC voltage bias.
Eqn. (20) divided by eqn.(19) implies: became dc bias independent 13 .By taking the non-zero crossing point at 1.63eV in the pure Y6 device, we obtain the Δμ ' value around 0.04 D. This small value might not directly reflect the dipole moment of the molecules with a preferred orientation, as both the populations of the randomly aligned and preferentially aligned molecules as well as the direction between the dipole moment and the electrical field are unknown.However, the increasing non-zero crossing spectral characteristics while increasing the loading ratio in Y6 devices strongly support that there is a preferred molecular orientation in the Y6 thin film.It is consistent with the GIWAXS results at different loadings of Y6, as shown in Supplementary Fig. 5 where a clear face-on orientation is revealed in the 2D patterns, and the results of recent MD simulations on a Y6 thin film 14 .
Supplementary Fig. 11a represent the charge transfer energies for excitation from M1 to M2 or vice versa.The effect of the electric field (F) is described as follows: Based on previous DFT calculations 7,18 , we used the following model parameters: Natural Transition Orbitals (NTOs) representing the hole and electron distributions in the lowest singlet excited state of dimer A of ITIC.Supplementary Fig. 4.b: Natural Transition Orbitals (NTOs) representing the hole and electron distributions in the lowest singlet excited states of dimer B of ITIC.

Supplementary Fig. 5 :
a-f 2D GIWAXS patterns of Y6 films and g, h corresponding GIWAXS intensity profiles along the in-plane and out-of-plane directions, respectively.The symbols *, #, and + represent the signals from PVK, Y6, and unclarified, respectively.Graphs i and j show the 2D GISAXS patterns from the synchrotron test and GISAXS intensity profiles along the in-plane (IP) direction, respectively.

Supplementary Fig. 6 :
Fitted absorption spectra of Y6 in a) CF solution (20-25 mg/ml), b) 10wt% Y6 in PVK, and c) 100wt% Y6 thin films with the Frank-Condon-weight density of states (FCWD) in the framework of Marcus-Levich-Jortner theory (detailed description in text).Dispersed phases containing non-interacting molecules are marked as 1 and 2 (colored in yellow).'Aggregate I' is marked as 3 and 6 (colored in red), and 'Aggregate II' is marked as 4 and 5 (colored in blue), respectively.Both have progressions in the low-energy (solid line) and high-energy (dashed line) regions.The global fit is indicated as a pink dashed line.

∝(
Δµ ( sin ωt)) in the first harmonic EA equation (eqn.13) is usually omitted in isotropic media where dipoles are randomly oriented.Δµ is a vector which will cancel out upon averaging the ensembles.In the manuscript, we use Δµ' to represent a preferred orientation of dipoles to avoid confusion with Δµ 2 .As EA is measured in transmission mode (T), where T = A − ΔT =A − .(−)ΔT = T .(−)∆T T = -Δα.d

:
First harmonic DC bias dependence EA Spectra of dispersed and pristine Y6 and ITIC thin films.The measured first harmonic EA signals at different loading ratios (10 wt% and 100 wt%) of a, b Y6 and c, d ITIC in a PVK matrix at different applied DC bias.The DC bias dependence of the first harmonic EA signals in 100 wt% Y6 shows asymmetric spectral characteristics.
; = 50 ; and 1 = 2 =100 meV.The energies of the eigenstates of the four-state model were calculated for ∆ − values in the range from 0.3 eV to -0.3 eV as a function of electric field.The  and p values were then derived by computing the first and second derivatives of the S1 energy as a function of electric field.

Table 1 :
Morphology parameters fitted by GISAXS profiles (ξ is the domain size of the amorphous phase).
 Optical absorption fitting using Frank Condon principle.

Table 2 :
Parameters used for the FC progressions at different loading ratios of Y6. ( T = 25.9 meV) 8upplementary Fig.7: Illustration of two distinct dimer configurations of Y6, labeled as A and B, extracted from the crystal structure reported from our previous work7and Dimer C (which closely resembles Dimer A) retrieved from the work by Marks and co-workers8.Both dimers A and C comprise asymmetric constituent monomers, whereas dimer B features symmetric constituent monomers.We replaced the long side chains with -CH3 groups for our calculations.A

λ=0.98 λ=0.94 λ=0.93 λ=0.88 electron hole S 1 S 2 S 3 S 4 Supplementary
Calculated energies for the lowest four singlet excited states (S1 to S4, denoted as ∆E) of dimer A of Y6, along with the corresponding oscillator strengths (f) for S0→Sn (n=1 to 4) transitions.The table also includes the variations in dipole moment (∆µ) and polarization (∆p) during these transitions.Additionally, similar values for the S1 state are provided for the constituent monomeric units (M1 and M2), comprising dimer A of Y6.Calculated energies for the lowest four singlet excited states (S1 to S4, denoted as ∆E) of dimer B of Y6, along with the corresponding oscillator strengths (f) for S0→Sn (n=1 to 4) transitions.The table also includes the variations in dipole moment (∆µ) and polarization (∆p) during these transitions.Additionally, similar values for the S1 state are provided for the constituent monomeric units (M1 and M2), comprising dimer B of Y6.
Fig. 8.a: Natural Transition Orbitals (NTOs) representing the hole and electron distributions in the lowest four singlet excited states of dimer A of Y6.Supplementary Fig. 8.b: Natural Transition Orbitals (NTOs) representing the hole and electron distributions in the lowest four singlet excited states of dimer B of Y6. 4 Supplementary Fig. 8.c: Natural Transition Orbitals (NTOs) representing the hole and electron distributions in the lowest four singlet excited states of dimer C of Y6.Supplementary Table3.a:SupplementaryTable3.b:

Table 3 . c :
Calculated energies for the lowest four singlet excited states (S1 to S4, denoted as ∆E) of dimer C of Y6, along with the corresponding oscillator strengths (f) for S0→Sn (n=1 to 4) transitions.The table also includes the variations in dipole moment (∆µ) and polarization (∆p) during these transitions.Additionally, similar values for the S1 state are provided for the constituent monomeric units (M1 and M2), comprising dimer C of Y6.
Supplementary Table4.a:Calculated energies for the lowest four singlet excited states (S1 to S4, denoted as ∆E) of dimer A of ITIC, along with the corresponding oscillator strengths (f) for S0→Sn (n=1 to 4) transitions.The table also includes the variations in dipole moment (∆µ) and polarization (∆p) during these transitions.Additionally, similar values for the S1 state are provided for the constituent monomeric units (M1 and M2), comprising dimer A of ITIC.

Table 4 . b :
Calculated energies for the lowest four singlet excited states (S1 to S4, denoted as ∆E) of dimer B of ITIC, along with the corresponding oscillator strengths (f) for S0→Sn (n=1 to 4) transitions.The table also includes the variations in dipole moment (∆µ) and polarization (∆p) during these transitions.Additionally, similar values for the S1 state are provided for the constituent monomeric units (M1 and M2), comprising dimer B of ITIC.